| Title:
|
Reconciliation of discrete and continuous versions of some dynamic inequalities synthesized on time scale calculus (English) |
| Author:
|
Sahir, Muhammad Jibril Shahab |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
28 |
| Issue:
|
3 |
| Year:
|
2020 |
| Pages:
|
277-287 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this paper is to synthesize discrete and continuous versions of some dynamic inequalities such as Radon's Inequality, Bergström's Inequality, Schlömilch's Inequality and Rogers-Hölder's Inequality on time scales in comprehensive form. (English) |
| Keyword:
|
Time scales |
| Keyword:
|
Radon's Inequality |
| Keyword:
|
Bergström's Inequality |
| Keyword:
|
Schlömilch's Inequality |
| Keyword:
|
Rogers-Hölder's Inequality. |
| MSC:
|
26D15 |
| MSC:
|
26D20 |
| MSC:
|
34N05 |
| idZBL:
|
Zbl 1473.26030 |
| idMR:
|
MR4197079 |
| . |
| Date available:
|
2021-03-03T08:58:10Z |
| Last updated:
|
2022-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148708 |
| . |
| Reference:
|
[1] Agarwal, R.P., O'Regan, D., Saker, S.H.: Dynamic Inequalities on Time Scales.2014, Springer International Publishing, Cham, Switzerland, MR 3307947 |
| Reference:
|
[2] Ammi, M.R.S., Torres, D.F.M.: Hölder's and Hardy's two dimensional diamond-alpha inequalities on time scales.Ann. Univ. Craiova, Math. Comp. Sci. Series, 37, 1, 2010, 1-11, MR 2609350 |
| Reference:
|
[3] Anderson, D., Bullock, J., Erbe, L., Peterson, A., Tran, H.: Nabla dynamic equations on time scales.Panam. Math. J., 13, 1, 2003, 1-48, MR 1953216 |
| Reference:
|
[4] Beckenbach, E.F., Bellman, R.: Inequalities.1961, Springer, Berlin, Göttingen and Heidelberg, MR 0158038 |
| Reference:
|
[5] Bellman, R.: Notes on matrix theory -- IV (An inequality due to Bergström).Amer. Math. Monthly, 62, 3, 1955, 172-173, MR 0072834, 10.2307/2306621 |
| Reference:
|
[6] Bergström, H.: A triangle inequality for matrices.In Den Elfte Skandinaviske Matematikerkongress (1949) Trondheim, Johan Grundt Tanums Forlag, Oslo, 1952, 264-267, MR 0053064 |
| Reference:
|
[7] Bohner, M., Peterson, A.: Dynamic Equations on Time Scales.2001, Birkhäuser Boston, Inc., Boston, MA, Zbl 0993.39010, MR 1843232 |
| Reference:
|
[8] Bohner, M., Peterson, A.: Advances in Dynamic Equations on Time Scales.2003, Birkhäuser Boston, Boston, MA, Zbl 1025.34001, MR 1843232 |
| Reference:
|
[9] Bătineţu-Giurgiu, D.M., Pop, O.T.: A generalization of Radon's inequality.Creative Math. & Inf., 19, 2, 2010, 116-121, MR 2761455 |
| Reference:
|
[10] Bătineţu-Giurgiu, D.M., Stanciu, N.: New generalizations and new approaches for two IMO problems.Journal of Science and Arts, 12, 1, 2012, 25-34, MR 2911825 |
| Reference:
|
[11] Bătineţu-Giurgiu, D.M., Mărghidanu, D., Pop, O.T.: A refinement of a Radon type inequality.Creat. Math. Inform., 27, 2, 2018, 115-122, MR 3885356, 10.37193/CMI.2018.02.03 |
| Reference:
|
[12] Hardy, G.H., Littlewood, J.E., Pölya, G.: Inequalities.1952, 2nd Ed., Cambridge, University Press, MR 0046395 |
| Reference:
|
[13] Hilger, S.: Ein Maßkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten.1988, Ph.D. Thesis, Universität Würzburg, Zbl 0695.34001 |
| Reference:
|
[14] Hölder, O.: Über einen Mittelwertsatz.Nachrichten von der Königlichen Gesellschaft der Wissenschaften und der Georg\-Augusts-Universität zu Göttingen, 1889, 38-47, |
| Reference:
|
[15] Mitrinović , D.S.: Analytic Inequalities.1970, Springer-Verlag, Berlin, MR 0274686 |
| Reference:
|
[16] Radon, J.: Theorie und Anwendungen der absolut additiven Mengenfunktionen.Sitzungsber. Acad. Wissen. Wien, 122, 1913, 1295-1438, |
| Reference:
|
[17] Sahir, M.J.S.: Hybridization of classical inequalities with equivalent dynamic inequalities on time scale calculus.The Teaching of Mathematics, XXI, 1, 2018, 38-52, MR 3782912 |
| Reference:
|
[18] Sahir, M.J.S.: Formation of versions of some dynamic inequalities unified on time scale calculus.Ural Math. J., 4, 2, 2018, 88-98, MR 3901588, 10.15826/umj.2018.2.010 |
| Reference:
|
[19] Sheng, Q., Fadag, M., Henderson, J., Davis, J.M.: An exploration of combined dynamic derivatives on time scales and their applications.Nonlinear Analysis: Real World Appl., 7, 3, 2006, 395-413, MR 2235865, 10.1016/j.nonrwa.2005.03.008 |
| . |
